Q. Two waves having equations $x_{1} = a\sin{\left( \omega t + \phi_{1} \right),}\ x_{2} = a\sin{(\omega t + \phi_{2})}$ If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is
A) $\pi/6$
B) $2\pi/3$
C) $\pi/4$
D) $\pi/3$
Explanation
(b) Superposition of waves does not alter the frequency of resultant wave and resultant amplitude
$\Rightarrow a^{2} = a^{2} + a^{2} + 2a^{2}\cos\phi = 2a^{2}(1 + \cos\phi)$
$\Rightarrow \cos\phi = - 1/2 = \cos{2\pi/3}\ \therefore\phi = 2\pi/3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.